Supeconductivity in the Pseudogap State in "Hot - Spots" Model: Ginzburg - Landau Expansion

We analyze properties of superconducting state (for both s-wave and d-wave pairing), appearing on the "background" of the pseudogap state, induced by fluctuations of "dielectric" (AFM(SDW) or CDW) short -- range order in the model of the Fermi surface with "hot spots". We present microscopic derivation of Ginzburg - Landau expansion, taking into account all Feynman diagrams of perturbation theory over electron interaction with this short - range order fluctuations, leading to strong electronic scattering in the vicinity of "hot spots". We determine the dependence of superconducting critical temperature on the effective width of the pseudogap and on correlation length of short - range order fluctuations. We also find similar dependences of the main characteristics of such superconductor close to transition temperature. It is shown particularly, that specific heat discontinuity at the transition temperature is significantly decreased in the pseudogap region of the phase diagram.